This is a comparison between mineos
and earth-flattened wavenumber integration synthetics (Computer
Programs in Seismology - 3.30 ) for the AK-135f
I use the same model for both sets of synthetics, except that the wavenumber integration model does not have an inner core [The reason for this is that my formulation for wavenumber integration only permits fluid layers at the top or at the bottom of the elastic stack but not sandwiched between two solid layers.
The program used for the conversion is conv.f and the starting model for an AK135-F continental is ak135-f. Running the program as
a.out < ak135-f
creates the files tak135-f.txt for mineos and
tak135sph.mod for the CPS programs.
This reformatting program does the following:
converts Q(kappa) Q(mu) used in free-oscillation code to Q(P) and Q(S) used in wavenumber integration code
reorders the AK-135-F model for mineos order, by converting from model as a function of increasing depth to one of increasing radius, and also converts from km, km/s, gm/cm3 to meters. m/s and kg/m3
replaces the gradient model of AK-135 by discrete layers. The layer velocity is obtained from the average of the slownesses at the depth points. A sharp velocity discontinuity is preserved. In effect this says that the slowness variation between two depths points is linear.
The model used for the wavenumber integration code is tak135sph.mod and the model used for mineos is tak135-f.txt. [Note on your browser, you may have to right-click and save-as for the files ending with .mod, since the browser may think that the file is a MOD music file].
The earth flattening mapping used in the CPS programs starts with the tak135sph.mod model and then internally performs the following steps, using the symbolism a for the radius of the Earth and r for the distance from the center of the Earth to a spherical shell.
Convert radius of a layer boundary to a depth using the transformation z = a ln(a/r)
Layer thicknesses are determined from the difference in z values for neighboring r values
The mid-layer radius is used for the velocity mapping, as vel(flat) = vel(sph)* ( a / (r0+r1)/2 )
The density mapping for P-SV potentials is rho(flat) = rho(sph) * ( a / (r0+r1)/2 ) ^ -2.275 (Biswas)
The density mapping for SH potentials is rho(flat) = rho(sph) * ( a / (r0+r1)/2 ) ^ -5 (Biswas and Knopoff)
Flat earth synthetics are multiplied by the scale factor sqrt[(dist/a)/sin(dist/a)] so that high frequency ray theory is satisfied for the geometrical spreading.
David Harkrider assisted with the density mapping for the P-SV problem. He demonstrated that the 2.275 was appropriate for the fundamental mode. This exercise focused on the entire waveform, which effectively tests the appropriateness for higher modes.
I assume that you already have Computer Programs in Seismology installed and that the PATH variable includes the absolute path to PROGRAMS.330/bin.
The tests performed consisted of comparing travel times, free-oscillation synthetics to wavenumber-integration synthetics that used Earth flattening, and a comparison of phase and group velocity dispersion between the free oscillation and plane-layer codes.
Last changed February 2, 2008